Given a real closed field $R$, we define a real algebraic manifold as an irreducible nonsingular algebraic subset of some $R^n$. This paper deals with deformations of real algebraic manifolds. The main purpose is to prove rigorously the reasonableness of the following principle, which is in sharp contrast with the compact complex case: “The algebraic structure of every real algebraic manifold of positive dimension can be deformed by an arbitrarily large number of effective parameters”.
Keywords:
given real closed field define real algebraic manifold irreducible nonsingular algebraic subset paper deals deformations real algebraic manifolds main purpose prove rigorously reasonableness following principle which sharp contrast compact complex algebraic structure every real algebraic manifold positive dimension deformed arbitrarily large number effective parameters
Affiliations des auteurs :
Edoardo Ballico
1
;
Riccardo Ghiloni
1
1
Department of Mathematics University of Trento 38123 Povo-Trento, Italy
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author = {Edoardo Ballico and Riccardo Ghiloni},
title = {The principle of moduli flexibility for
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Edoardo Ballico; Riccardo Ghiloni. The principle of moduli flexibility for
real algebraic manifolds. Annales Polonici Mathematici, Tome 109 (2013) no. 1, pp. 1-28. doi: 10.4064/ap109-1-1
